Physical Chemistry Third Edition

1014 24 Magnetic Resonance Spectroscopy

CCl 2. Assume that the chlorines are both^35 Cl, which

has a spin quantum number of 3/2.

24.15Describe the ESR spectrum of the ethyl radical,
CH 3 CH− 2. Make a reasonable assumption about
the orbital in which the unpaired electron is
found.

24.16Assume that the methyl radical is planar (it is known to be
nearly but not quite planar). Describe the ESR spectrum
of the molecule.

24.17Compare the ESR spectra of an isolated H atom with that
of an isolated He+ion. Assume that the He nucleus is

(^4) He, which hasI0.
24.18The Hückel molecular orbital method gives the following
LCAOMO for the unpaired electron in the naphthalene
negative ion:
ψ 0 .42536(−ψ 1 +ψ 4 −ψ 5 +ψ 8 )+ 0. 26286
(−ψ 2 +ψ 3 −ψ 6 +ψ 7 )
whereψiis the unhybridizedporbital on carbon number
i, numbered as in the diagram:
81
7 2
6 3
5 4
Assume that the coupling constant for each hydrogen
is approximately proportional to the square of the
coefficient for the carbon on which the hydrogen is
bonded, and describe the ESR spectrum of the
naphthalene negative ion.
24.19For electrons in a magnetic field such that ESR absorption
occurs at a frequency of 9. 159 × 109 s−^1 , calculate the
ratio of the populations of the two spin states at 298 K.
24.20For electrons in a magnetic field of 1.44 T, calculate the
ratio of the populations of the two spin states at 298 K.

24.4 Nuclear Magnetic Resonance Spectroscopy

Nuclearmagneticresonance(NMR)spectroscopy exploits transitions between different

nuclear spin states in a magnetic field. It is the most important tool for determining

the structure of organic molecules, and the 2003 Nobel Prize in medicine was awarded

to chemist Paul C. Lauterbur and physicist Peter Mansfield for inventingmagnetic

resonance imaging (MRI), which is used in medicine to obtain images of internal

organs of patients through their differing densities of hydrogen atoms by focusing on

the NMR absorption of hydrogen nuclei.^2

Older NMR instruments are “continuous-wave” instruments. Radio-frequency

energy is conducted by coaxial cable to the sample, which is located in the magnetic

field of an electromagnet. The radiation can cause magnetic dipole transitions between

different nuclear spin states. Since electromagnets cannot scan over a large range of

magnetic fields without losing the necessary field homogeneity, a scanning instrument

operates at a fixed magnetic field and the frequency of the radiation is scanned. The

most common continuous-wave instruments obtain proton NMR spectra, but some are

built to obtain spectra of two or more nuclei.

Most modern NMR instruments are Fourier transform NMR spectrometers,

which frequently use superconducting electromagnets. Such instruments can obtain

spectra of more than one kind of nucleus, and can obtain a spectrum more quickly

than can a scanning instrument. They can also perform specialized experiments that

are impossible with scanning instruments. The spectra that we now discuss are the

same whether they are generated by a continuous-wave or a Fourier transform

instrument.

(^2) See C. G. Fry,J. Chem. Educ., 81 , 922 (2004) for a historical account.